Place the garlic and shallots on a sheet of foil and drizzle with the oil. Season with salt and pepper, wrap completely in foil, and roast about 1 hour.
Let the garlic and shallots cool completely before unwrapping.
Squeeze the cooled garlic cloves and shallots from their skins into a mixing bowl and mash into a smooth paste with a fork.
Add the remaining ingredients and stir until fully combined. Season with salt and pepper and stir again.
Cover and refrigerate at least 1 hour (up to 12 hours is better) to let the flavors come together.
Serve with crusty bread, crostini, and/or crudite.